\(\left(\frac{1}{8}\right)^x=\frac{1}{64}\)
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S
1
EC
12 tháng 9 2016
\(\left(\frac{1}{64}\right)^x=\left(-\frac{1}{8}\right)^{14}\)
\(\left(\frac{1}{64}\right)^x=\left[\left(-\frac{1}{8}\right)^2\right]^7\)
\(\left(\frac{1}{64}\right)^x=\left(\frac{1}{64}\right)^7\)
\(\Rightarrow x=7\)
P1
6 tháng 8 2017
Câu b thôi các bạn nhé, câu a mình ko cần nx với cả mình ghi sai dữ liệu câu a r
DP
6 tháng 8 2017
a, \(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot\frac{4}{10}\cdot...\cdot\frac{30}{62}\cdot\frac{31}{64}=2x\)
\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot4\cdot...\cdot30\cdot31}{4\cdot6\cdot8\cdot10\cdot...\cdot62\cdot64}=2x\)
\(\Leftrightarrow\frac{1\cdot2\cdot3\cdot4\cdot...\cdot30\cdot31}{2\cdot2\cdot3\cdot2\cdot4\cdot2\cdot5\cdot2\cdot....\cdot31\cdot2\cdot32\cdot2}=2x\)
\(\Leftrightarrow\frac{1}{2\cdot2\cdot2\cdot2\cdot....\cdot2\cdot2\cdot32}=2x\)
Có : (31 - 1) : 1 + 1 = 31 (thừa số 2)
\(\Rightarrow\frac{1}{2^{31}.32}=2x\)
\(\Rightarrow x=\frac{1}{2^{31}.32}\div2\)
b, \(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\)
\(\Leftrightarrow x+1=x+4\)
\(\Leftrightarrow0=3\text{ (vô lý) }\)
20 tháng 5 2018
a)\(\left(x-1\right)^{x+2}=\left(x-1\right)^{x+4}\Leftrightarrow\left(x-1\right)^{x+2}\left[\left(x-1\right)^2-1\right]=0\Leftrightarrow x\left(x-1\right)^{x+2}\left(x-2\right)=0\)
Do đó \(x\in\left\{0;1;2\right\}\)
25 tháng 7 2018
b)
\(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot...\cdot\frac{31}{64}=2^x\Leftrightarrow\frac{1\cdot2\cdot3\cdot...\cdot31}{4\cdot6\cdot8\cdot...\cdot64}=2^x\Leftrightarrow\frac{31!}{\left(2\cdot2\right)\cdot\left(2\cdot3\right)\cdot\left(2\cdot4\right)\cdot...\cdot\left(2\cdot31\right)\cdot64}=2^x\)
\(\frac{31!}{2^{30}\cdot31!\cdot2^6}=2^x\Leftrightarrow\frac{1}{2^{36}}=2^x\Leftrightarrow2^{-36}=2^x\Rightarrow x=-36\)
20 tháng 10 2016
a) \(\left(\frac{2}{3}:x+\frac{1}{4}\right)^2=\frac{49}{64}\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}\left(\frac{2}{3}:x+\frac{1}{4}\right)^2=\left(\frac{7}{8}\right)^2\\\left(\frac{2}{3}:x+\frac{1}{4}\right)^2=-\left(\frac{7}{8}\right)^2\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}\frac{2}{3}:x+\frac{1}{4}=\frac{7}{8}\\\frac{2}{3}:x+\frac{1}{4}=-\frac{7}{8}\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}\frac{2}{3}:x=\frac{5}{8}\\\frac{2}{3}:x=-\frac{9}{8}\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=\frac{16}{15}\\x=-\frac{16}{27}\end{array}\right.\)
20 tháng 10 2016
b) \(\frac{2}{5}:\left|x-2\right|-\frac{1}{3}=\frac{1}{2}\)
\(\Leftrightarrow\frac{2}{5}:\left|x-2\right|=\frac{5}{6}\)
\(\Leftrightarrow\left|x-2\right|=\frac{12}{25}\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x-2=\frac{12}{25}\\x-2=-\frac{12}{25}\end{array}\right.\)
\(\Leftrightarrow\left[\begin{array}{nghiempt}x=\frac{62}{25}\\x=\frac{38}{25}\end{array}\right.\)
8 tháng 7 2016
a) \(14:\frac{0,4x+0,6}{x}=7\)
\(\frac{0,4x+0,6}{x}=2\)
0,4x + 0,6 = 2.x
2x - 0,4x = 0,6
1,6x = 0,6
x = 0,375
b) \(\left(160\%+\frac{2}{3}x-x\right).12=660\)
\(\left(160\%+\frac{2}{3}x-x\right)=55\)
\(x\left(\frac{2}{3}-1\right)=53,4\)
\(-\frac{1}{3}x=\frac{267}{5}\)
\(x=\frac{267}{5}.\frac{3}{-1}\)
\(x=-160,2\)
c) \(1:\frac{1.2.3.4.....31}{2.2.2.3.2.4.....2.32}=2^x\)
\(1:\frac{1.2.3.4.....31}{2^{31}.2.3.4.....31.2^5}=2^x\)
\(1:\frac{1}{2^{36}}=2^x\)
\(2^{36}=2^x\)
\(x=36\)
S
19 tháng 3 2020
a) \(\left(-\frac{3}{4}\right)^{3x-1}=\frac{-27}{64}\)
\(\Leftrightarrow\left(-\frac{3}{4}\right)^{3x-1}=\left(-\frac{3}{4}\right)^3\)
\(\Leftrightarrow3x-1=3\)
\(\Leftrightarrow3x=4\)
\(\Leftrightarrow x=\frac{4}{3}\)
b) Đề sai ! Sửa :
\(\left(\frac{4}{5}\right)^{2x+5}=\frac{256}{625}\)
\(\Leftrightarrow\left(\frac{4}{5}\right)^{2x+5}=\left(\frac{4}{5}\right)^4\)
\(\Leftrightarrow2x+5=4\)
\(\Leftrightarrow2x=-1\)
\(\Leftrightarrow x=-\frac{1}{2}\)
c) \(\frac{\left(x+3\right)^5}{\left(x+5\right)^2}=\frac{64}{27}\)
\(\Leftrightarrow\left(x+3\right)^3=\left(\frac{4}{3}\right)^3\)
\(\Leftrightarrow x+3=\frac{4}{3}\)
\(\Leftrightarrow x=-\frac{5}{3}\)
d) \(\left(x-\frac{2}{15}\right)^3=\frac{8}{125}\)
\(\Leftrightarrow\left(x-\frac{2}{15}\right)^3=\left(\frac{2}{15}\right)^3\)
\(\Leftrightarrow x-\frac{2}{15}=\frac{2}{15}\)
\(\Leftrightarrow x=\frac{4}{15}\)
\(\left(\frac{1}{8}\right)^x=\left(\frac{1}{8}\right)^2\)
\(\Rightarrow x=2\)
Vậy \(x=2\)
\(\left(\frac{1}{8}\right)^x=\frac{1^2}{8^2}\)
\(\left(\frac{1}{8}\right)^x=\left(\frac{1}{8}\right)^2\)
\(\text{Vậy }x=2\)